A high melting metal such as tungsten and molybdenum is formed into projections and an electric field is applied to the ends of the projections in a vacuum from the outside, so that electrons induced to the ends of the metal are emitted to the outside. Generally, the metal projections are called emitters and the emission of electrons from the emitters is called field emission or field radiation.
Elements for emitting electrons through the field emission are called field-emission electron source elements or cold-cathode electron source elements and have been recently used in various fields. For example, the elements are used as the electron sources of electron microscopes instead of hot filaments of the prior art, and are used as fluorescent display tubes that are opposed to electron source elements and emit light from phosphors by drawing electrons into anode electrodes on which phosphor films are formed.
In many cases, emitters have small structures and a single emitter cannot obtain a sufficient amount of current. Thus a group of emitters is used to obtain a sufficient amount of current. In the present specifications, a group of emitters is called “cold-cathode electron source elements”.
Further, field emission displays have become practical in which cold-cathode electron source elements are arranged in a matrix to constitute a cold-cathode electron source array, anode electrodes on which phosphors corresponding to RGB are formed are disposed on the opposed side, and electrons through field emission are drawn to the anode electrodes so as to emit light from the phosphors. The following will describe, as an example, an FED using Spindt-type emitters shown in FIGS. 9 and 10.
The FED is configured such that a cathode substrate 101 and an anode substrate 111 are opposed to each other.
On the surface of the cathode substrate 101, stripe emitter signal wires 102a are formed in parallel and a gate insulating film 103 is formed so as to cover the emitter signal wires 102a. On the surface of the gate insulating film 103, stripe gate signal wires 104a are formed so as to cross the emitter signal wires 102a. 
On the gate signal wires 104a and the gate insulating film 103, a plurality of openings 104b are formed in a region where the gate signal wires 104a and the gate insulating film 103 cross the emitter signal wires 102a. In the respective openings 104b, emitters 105 are formed so as to be disposed on the emitter signal wires 102a. The openings 104b on the surfaces of the gate signal wires 104a act as gate electrodes. An electric field is applied to the gate electrodes 104b through the gate signal wires 104a, so that electrons can be emitted from the ends of the emitters 105. A region where the multiple emitters 105 and the gate electrodes (=the openings 104b) are formed is called a cold-cathode electron source element region.
The anode substrate 111 has a surface opposed to the cathode substrate 101, and an anode electrode 112 made up of a transparent conductive film (ITO) is formed over the opposed surface of the anode substrate 111. On the anode electrode 112, phosphors 113R, 113G, and 113B of red, green, and blue are sequentially formed in stripe. The phosphors 113R, 113G, and 113B are formed in parallel with the gate signal wires 104a formed on the cathode substrate 101.
In the FED configured thus, electron emission from the multiple electron source elements arranged in a matrix is sequentially controlled based on output signals from a video circuit, so that a desired image can be displayed on the surface of the anode substrate 111.
In the same configuration, a photoelectric conversion film (not shown) may be formed instead of the phosphors 113R, 113G, and 113B on the surface of the anode substrate 111, so that image elements can be configured to read hole-electron pairs, which have been induced by external light, by electrons emitted from electron source elements.
In an FED and an image element, light emission or the resolution of imaging is determined depending upon the area of electrons on the surface of an anode electrode, the electrons having been emitted from an electron source element. Thus in order to obtain an FED and an image element with a high resolution, a solution is to reduce the area of the electron emission surface of an electron source element. However, when an electron source element is excessively reduced in area, an emission current decreases and a necessary amount of current cannot be obtained.
Further, electrons from the cold-cathode electron source are not all emitted straight to the anode electrode 112 but are expanded to a certain degree. This is because the ends of the emitters 105 constituting the electron source each have a certain radius of curvature in the manufacturing process. Since electrons are emitted perpendicularly to a curvature surface, electron beams are emitted so as to spread to a certain degree.
For this reason, in order to obtain electron beams spreading with an area corresponding to a resolution on an anode surface (=the surface of the anode substrate 111), it is necessary to suppress the expansion of electrons emitted from the electron source or prevent excessively spreading electrons from reaching the anode surface. A technique for the former condition is called a convergence technique of electron beams and a technique for the latter condition is called a trimming technique. Such techniques are reported in patent document 1, patent document 2, and so on.
Patent document 1 and patent document 2 describe convergence techniques in which a mesh electrode is provided between an electron source element and an anode electrode, electrons are drawn from the electron source element by applying a predetermined voltage to the mesh electrode, and electron beams from the mesh electrode to an anode surface are substantially aligned in a normal direction.
Patent documents 3 and 4 of the present inventor describe techniques in which out of electron beams emitted from an electron source, electron beams in a normal direction are selectively passed by forming an electric field distribution in a mesh structure, thereby suppressing the expansion of the electron beams on an anode surface.    Patent document 1: Japanese Patent Laid-Open No. 2000-048743    Patent document 2: Japanese Patent Laid-Open No. 2005-228556    Patent document 3: Japanese Patent Laid-Open No. 2007-250531    Patent document 4: Japanese Patent Laid-Open No. 2007-250532